The cortical dorsal auditory stream has been proposed to mediate mapping between auditory and articulatory-motor representations in speech processing. Whether this sensorimotor integration contributes to speech perception remains an open question. Here, magnetoencephalography was used to examine connectivity between auditory and motor areas while subjects were performing a sensorimotor task involving speech sound identification and overt repetition. Functional connectivity was estimated with inter-areal phase synchrony of electromagnetic oscillations. Structural equation modeling was applied to determine the direction of information flow. Compared to passive listening, engagement in the sensorimotor task enhanced connectivity within 200 ms after sound onset bilaterally between the temporoparietal junction (TPJ) and ventral premotor cortex (vPMC), with the left-hemisphere connection showing directionality from vPMC to TPJ. Passive listening to noisy speech elicited stronger connectivity than clear speech between left auditory cortex (AC) and vPMC at ~100 ms, and between left TPJ and dorsal premotor cortex (dPMC) at ~200 ms. Information flow was estimated from AC to vPMC and from dPMC to TPJ. Connectivity strength among the left AC, vPMC, and TPJ correlated positively with the identification of speech sounds within 150 ms after sound onset, with information flowing from AC to TPJ, from AC to vPMC, and from vPMC to TPJ. Taken together, these findings suggest that sensorimotor integration mediates the categorization of incoming speech sounds through reciprocal auditory-to-motor and motor-to-auditory projections.